In this appendix, we list the finite sum identities useful in simplifying the summations in appendix A. Except for the identity eq:B5 that seems new, the others can be found in [1]}, [2]}, [3]}, [4]}, [5]}.
Here, it is sufficient to set \(a,b\ge 0, a\ne b\)  in identities eq:B1–eq:B3, eq:B6–eq:B7, and \(a>m\)  in eq:B8. The derivation of the identity eq:B5 is provided in the end of this appendix.
\(\sum _{k=1}^{m}\psi _{0}(k+a)=(m+a)\psi _{0}(m+a+1)-a\psi _{0}(a+1)-m\) 
\(\sum _{k=1}^{m}\psi _{1}(k+a)=(m+a)\psi _{1}(m+a+1)-a\psi _{1}(a+1)+\psi _{0}(m+a+1)-\psi _{0}(a+1)\) 
\(\sum _{k=1}^{m}\frac{\psi _{0}(k+a)}{k+a}=\frac{1}{2}\left(\psi _{1}(m+a+1)-\psi _{1}(a+1)+\psi _{0}^{2}(m+a+1)-\psi _{0}^{2}(a+1)\right)\) 
\(\sum _{k=1}^{m}\frac{\psi _{0}(m+1-k)}{k}=\psi _{0}^{2}(m+1)-\psi _{0}(1)\psi _{0}(m+1)+\psi _{1}(m+1) -\psi _{1}(1)\) 
\(\sum _{k=1}^m \frac{\psi _0 (m+1+k)}{k}=\psi _0^2(m+1)-\psi _0(1) \psi _0(m+1)-\frac{1}{2} \psi _1(m+1)+\frac{\psi _1(1)}{2}\) 
\(\sum _{k=1}^{m}\psi _{0}(k+a)\psi _{0}(k+b)&=&(b-a) \sum _{k=1}^{m-1} \frac{\psi _0(a+k)}{b+k}+(m+a) \psi _0(m+a) \psi _0(m+b)-a\times \nonumber \\&& \psi _0(a+1) \psi _0(b+1)-(m+a-1) \psi _0(m+a)+a \psi _0(a+1)-\nonumber \\&&(m+b) \psi _0(m+b)+(b+1) \psi _0(b+1)+2 m-2\) 
\(\sum _{k=1}^{m}\frac{\psi _{0}(k+b)}{k+a}=&-\sum _{k=1}^{m}\frac{\psi _{0}(k+a)}{k+b}+\psi _{0}(m+a+1)\psi _{0}(m+b+1)-\psi _{0}(a+1)\times \nonumber \\&\psi _{0}(b+1)+\frac{1}{a-b}(\psi _{0}(m+a+1)-\psi _{0}(m+b+1)-\psi _{0}(a+1)+\nonumber \\&\psi _{0}(b+1))\) 
\(\sum _{k=1}^{m}\frac{\psi _{0}(a+1-k)}{k}=&-\sum _{k=1}^{m}\frac{\psi _{0}(k+a-m)}{k}+(\psi _{0}(a-m)+\psi _0(a+1))(\psi _{0}(m+1)-\nonumber \\&\psi _{0}(1))+\frac{1}{2}\left((\psi _{0}(a-m)-\psi _{0}(a+1))^2+\psi _{1}(a+1)-\psi _{1}(a-m)\right) \nonumber \\\) 
